Project Summary: The 2014 Chemistry Nobel Prize was awarded for advances in ?uorescent labeling, instrumentation and anal- ysis methods which together, over the last decade, have resolved particle positions to within ?20-30 nm. That is, below the diffraction limit of light used to excite them. Superresolution has subsequently been used to image ?-amyloid ?bers tied to neurodegenerative disorders and directly observe diffraction limited protein clustering linked to cancer phenotypes. While superresolved localization reveals static cellular structures of immediate relevance to health, it does not provide direct insight into disease dynamics. Directly observing in vivo dynamics at the single molecule level demands multi-particle superresolved particle tracking. Superresolved tracking is more dif?cult than superresolved localization because ? for the same number of photons collected ? tracking requires mobile particles to be localized over multiple image frames. Furthermore, multi-particle superresolved tracking re- quires that this all be done while accounting for unavoidable overlapping particle trajectories within a con?ned cellular volume a few diffraction limited volumes in size. Thus, to date, there is no systematic way to accurately track more than one protein, of the millions of proteins, inside a volume the size of E. coli?s cytoplasm at once. The overarching goal is therefore: To provide the ?rst principled multi-particle superresolved track- ing algorithm by exploiting the novel tools of Bayesian nonparametrics (BNPs) that have already deeply impacted Data Science over the last decade. BNPs can learn particle numbers in each frame and particle trajectories across all frames in a computationally tractable manner in a way that is directly informed by the data (photons collected per pixel). The tracking method developed will be applied to multi-particle problems ? such as the assembly/disassembly of serine chemoreceptor, Tsr, complexes on E. coli?s inner membrane ? and problems involving abrupt dynamical changes ? such as transitions between bound/unbound states of RNA polymerases ? naturally dealt with in the principled tracking framework proposed. Two Speci?c Aims are proposed. Speci?c Aim I ? Develop the very ?rst, fully-integrated and unsupervised, superresolved tracking algorithm for multiple diffraction-limited particles under the assumption that particles diffuse with a single (unknown) diffusion coef?cient. Speci?c Aim II ? Repeat Speci?c Aim 1 for the case where dynamical models according to which particles evolve are unknown or even changing in time (that is, the restriction that dynamics be governed by simple diffusion is lifted). Within each Aim, we will: determine particle numbers in each frame by adapting (nonparametric) Bernoulli processes; adapt observation models to account for complex label photophysics and aliasing artifacts important for fast-moving particle; treat particle con?nement for particle diffusion in small bacterial cells while learning dynamical models by adapting Dirichlet processes; incorporate detailed camera noise models.